BSPM (Body Surface Potential Mapping) is a relatively new technique for the study and analysis of the electrical activity of the heart. In contrast to the standard ECG technique, in which the heart activity is measured by the 12 standard leads, the information about the heart in the BSPM method is obtained from all over the thorax, by placing an array of many electrodes (usually 120-240 in number) on the body of the subject. Since the data is recorded simultaneously from all electrodes, this technique is capable of providing sensitive information (see [1] and its references) concerning electrical events in the heart and enables better spatial resolution in locating the cardiac generators [2,3].
However, despite the improved spatial resolution and sensitivity of the BSPM method, utilization of BSPM is limited to a small number of laboratories. Three main reasons were pinpointed by Mirvis in [1]:1) There are various alternative techniques, such as echocardiography, CT and MRI, which provide noninvasively useful clinical information; 2) The technical complexity and the price of custom-designed multielectrode BSPM system, which includes sophisticated multiplexing, amplification, filtering, sampling and storage units; 3) The vast amount of raw data obtained by BSPM, which requires long processing times as well as a new form of graphical representation.
Many studies explored partial solutions for the two last problems. Almost all studies take advantage of the statistical properties of the electrocardiographic signals, in order to reduce the system complexity and the amount of measured data.
The statistical properties of the ECG signals were studied by Favella et al. in [4], who showed that the electrical potentials projected on the thorax may be treated as samples of a stochastic process defined by the autocorrelation kernel: EQU R(z,z')=E[(F(z)-f(z)) (F*(z')-f*(z'))] (1)
where *--is complex conjugate, z=(x,y)--are coordinates on the thorax, F(z)--is a random field, with some probability measure, E[ ]--is the expectation of an ensemble of samples at the moment t.sub.0 and f (z)=E[F (z)].
Eigenfunctions of R (z,z') are usually used in compression protocols of BSPM data. Horan et al. [5], studied the ECG waveform by the means of Principal Factor Analysis. Ahmed and Rao compared different ECG compression methods based on orthogonal expansions and found that when reconstructing the signal from 16 coefficients of Karhunen-Loeve (K-L) expansion, the mean square error is approximately two times lower than by Discrete Cosine Transform [6]. Compression of potential maps in the spatial domain, was investigated by Lux et al. [8]. Their results show that the reconstruction of a map is obtained by means of 12 eigenfunctions for the QRS period and by 30 eigenfunctions for the whole QRST with up to 2% RMS error, whereas temporal compression [9] of the spatially reduced BSPMs, required 18 expansion coefficients.
One of the most difficult problems in BSPM compression by the expansion on an eigenfunction basis, is the need to compute and decompose very large covariance matrices. Uijen et al. [10], used the SVD method and showed an efficient way to circumvent this computation obstacle. In their study, the authors used only 36 first coefficients of K-L decomposition for the reconstruction of the BSPM within the 73 .mu.V RMS error limit during the QRS phase.
Statistical methods, other than K-L expansion, are utilized in a sequential algorithm, based on covariance matrix analysis, for finding the optimal locations of a reduced electrode set on the thorax [11]. Thirty electrodes are used to produce an estimation (by the linear transform) of a whole rectangular electrode grid within the correlation of 0.98 and the RMS error of the order of the system noise.
BSPM compression has also been performed on the deterministic orthogonal basis. A more extended function basis is required to produce the same reconstruction quality, but other advantages may be gained. Balossino et al. [12] utilize a basis of spherical harmonies, where rotational invariance of the measurement system is achieved. Thus the measurement is less sensitive to the directional alignment of the electrodes, which are usually mounted on a jacket worn by the patient. The body size also becomes an invariant parameter. This reduces the drawbacks of applying the BSPM in the clinic.
In the reports described above, the BSPM measurement is simplified and its data compressed by reducing the number of electrodes, while allowing some predefined small statistical error. Still, the simplified system includes rather complex analog electronic units. Furthermore, the information content provided by each one of the remaining electrodes becomes critical, therefore requiring a more accurate and expensive instrumentation.
The present invention describes a new approach based on implementing level-crossing electrodes for simplifying the BSPM measurement system and concurrently compressing the data. To utilize this approach a novel algorithm for reconstruction from level-crossings (LC) is developed. The electrodes in the suggested system are used only for detecting the times when the incoming ECG signal crosses some given voltage level. This partial data provides information for reconstruction of the original BSPM. As shown later, the LC data is sufficient for the reconstruction of the BSPM and therefore the complexity of the measurement system may be significantly reduced. The compression of the BSPM is achieved as well, since the level-crossing electrodes provide only a few samples per cardiac cycle for each electrode.